The number of ways of getting 40 heads in 100 coin tosses is given by the expression 100C40 (combination, so the order is not important). There are 2^100 possible results from tossing 100 coins ranging from 100 heads in a row to 100 tails in a row. That's about 1.268*10^30. 100C40 is calculated thus:
(100*99*98*97...62*61)/(1*2*3*4...39*40) which when evaluated is 1.3746*10^28, sometimes written 1.3746E28. It's an approximate number. To get the probability we divide the number of ways of getter exactly 40 heads by the total number of possibilities, so that's 100C40/2^100=0.0108, or just over 1%.
But we want to know the probability of getting between 40 and 60 heads in 100 tosses. So we have to add to this 100C41/2^100 + 100C42/2^100 + 100C43/2^100 +...+100C60/2^100. 2^100 is a common factor so we could add all the combinations first then divide by this common factor. This computes to 1.223*10^30/2^100=0.9648, or 96.48%.
This can also be solved by calculating the area under the probability curve, but that's for another day!